So to start with your initial question, that depends on what you mean by "similarity of their religion." Because the religion practised by Turkic peoples varied from region to region and location to location.

Generally speaking, it's thought that the steppe nomads before the Mongols, including the Xiongnu/Huns, the Gok-Turks, etc. generally practiced a shamanistic religion known as Tengriism (I won't get into the details because we don't know too much about Tengriism before the Mongols, and I don't really study that part). However, in the hinterlands of agricultural civilizations, many worshipers of many religions could be found, so it's important to take a look at what Bactria and Sogdia were like when Islam first arrived to the region in the mid-600's AD.

The cultural landscape of Bactria, Sogdia, Xinjiang, Ferghana, and the rest of Central Asia was rather diverse. You still had remnants of the Huns and other Oghuric-speaking proto-Turkic peoples floating around, and the steppes were at the time dominated by the Eastern and Western Gok-Turkic Khaganates. Much of farther Sogdia and Baktria's cities such as Samarkand, etc. had fallen out of Sassanid control as the Sassanian Persians caved in on themselves during the expansion of the Rashidun Caliphate. Most of the region was by and large Zoroastrian, the official religion of Persia, but other religions were extremely prominent at the time, including Buddhism. There were also pockets of various forms of Christianity, Manichaeism, Judaism, Hinduism, etc. throughout the region. Many of these religions had a habit of melding together and becoming their own local sects. As a result of trade, many of these sects spread to the various Turkic-speaking peoples that were expanding out from the Altai mountains at the time. So many Turks in the region practiced Buddhism, etc. Some in the Caucasus region had also converted to Christianity, such as the Caucasian Huns. Judaism was also prominent in the Caspian region and would become a major factor in the politics of the Khazars (although it's kind of an overstatement to say they were a "Jewish state.")

So to some degree you could say that Islam was similar to some of the religions penetrating the Turkic sphere (Manichaeism, Christianity, and Judaism were all Abrahamic religions like Islam), but Tengriism was very different from Islam, being a shamanistic religion, and Buddhism was also radically different from Islam.

Islamization of Central Asia ultimately began with the conquest of Bactria and Sogdia, which technically started with the fall of Marv in 651, but was stalled by the internal conflicts that wracked the Rashidun and early Umayyad Caliphates. The formal conquest began in 705, and lasted until 751, with the rather infamous Battle of Talas. However, Chinese control of the Silk Road city states beyond Xinjiang was wrenched out of their hands moreso due to the An Lushan rebellion than to that particular battle, as the Arabs never pressed their strategic advantage. Regardless, within these conflicts could be found many Turkic-speaking princes, and the Eastern Gokturk Khaganate itself did get involved on several occasions, usually fighting alongside the Chinese. But the primary Turkic people involved in these conflicts were the Karluks (Qarluqs).

The Karluks were by and large the first Turkic people to begin embracing Islam, and this was mostly done through their trade relations with the Abbasid Caliphate, which now controlled the Central Asian city states. Although certainly the Abbasids fought many armed conflicts with the Turkic peoples, none of them were really hell-bent on forced conversion and conquest and the spread of Islam into the region was slow. For example the dominant religion among one of the major Turkic powers of the 700's, the Uyghurs, was Manichaeism. It was the translation of the Quran into Middle Persian, Sogdian, Bactrian, and the other Central Asian Indo-Iranian and Tocharian languages that resulted in Islam's rapid spread into the Turkic population, as well as Xinjiang, and this was spread primarily through trade relationships and general cultural exchange, not military force. The Karluks would eventually reform themselves into the Kara-Khanids, and many naturally converted to Islam en-masse because their ruler converted. But that did not make it the dominant religion among the Turkic or Mongolic peoples as a whole. However, they are more or less the first Turkic people who adopted it as their primary religion.

The modern Turks are another matter. The modern Turks partially descend from the Seljuks, who were a part of the Oghuz confederacy (Oghuz meaning "Clan" or "Arrow" in Common Turkic, being the compatriot to "Oghur" which is the other branch of the Turkic language, Old Turkic). They emigrated into Khosaran some time in the 10th century and allegedly converted to Islam around 985. After a few decades of fighting the Ghaznavid Empire, they immigrated into Persia working with the declining Abbasids and established their own Empire, expanding and settling first in Caucasian Albania (Azerbaijan) and then conquering much of Armenia. Obviously they then went to war with the Romans ("Byzantines"), eventually defeating them at Mantzikert in 1071, and then exploiting the political infighting to enter into Anatolia. So to a certain extent you could argue the conquest of Anatolia, and the Anatolian Greek and Armenian Populations, was a conquest that resulted in their conversion to Islam, but that still took a long time to convert the Orthodox Roman population and change their identity from Roman to Turkic. However, this latter part is outside my area (Xiongnu/Huns, 4th-7th century Rome, and to some extent early Turks) so I hope someone with more knowledge on the Turkic conquest and assimilation of Anatolia and the collapse of Roman Anatolia can provide a good follow up elaborating on this part.

I hope this answers at least part of your question.

Sources:

Sinor, Denis. The Cambridge History of Early Inner Asia. (Cambridge: Cambridge University Press, 1990).

Findley, Carter Vaughn. The Turks in World History. (Oxford: Oxford University Press, 2003).